Saanchi Goyal, 3, and Harry, 4, were looking out through the sunroof of their cars in different parts of Delhi when sharp strings slit their throats.
Zafar Khan, 22, died in the same manner when he was riding his motorbike.
Glass-coated strings are used to bring down competitors’ kites, but they also end up injuring and killing people.
Many Indians fly kites to celebrate festivals and important occasions like the Independence Day, which is celebrated on 15 August.
But every year, there are reports of people dying or getting wounded from the kite strings – locally known as manja – treated with powdered glass or metal to sharpen them.
Similar strings killed a five years old boy in 2014 in the northern town of Moradabad, and a five-year-old girl died in Jaipur in 2014.
These strings also kill and maim hundreds of birds annually – at least 500 birds have been admitted to the Charity Birds Hospital in Delhi in the past three days alone, Indian media reports say. The hospital says it treats up to 8,000 birds every year.
On Monday, a policeman in Delhi was also injured from a sharpened string.
The Delhi government has now banned the use of sharpened manja to fly kites and promised to run campaigns to educate people about the dangers of using such strings.
Authorities said the sale, production and storage of nylon, plastic or any other glass or metal-coated manja would be prohibited in the capital city and those who violated the ban would have to pay a penalty of 100,000 rupees ($1,495; £1,148) and could be jailed for up to five years.